A safe falls from rest from the top of a 37 m high cliff towardWiley Coyote, who

Question

A safe falls from rest from the top of a 37 m high cliff towardWiley Coyote, who is standing at the base. Wiley first notices thesafe after it has fallen 12.6 m. The acceleration of gravity is 9.8m/s2 . How long does he have to get out of the way? Answer in unitsof s.

I thought I had the answer by doing the following:
x=xo + vot + .5 a t2
-37=-4.9 t2
t = 2.747912009

-24.4=-4.9 t2
t = 2.231499907

and then subtracting the two to get.... .516412016 s
But the answer is put into an online system and it will not takethis number as an answer.
Any help would be appreciated.

Explanation / Answer

You are correct in that the total time it takes to fall is t =2.747912009s. However, when you calculate the time it hastaken to get to fall 12.6 m, you should have used -12.6m (thedistance from where it was released to the point it is at now)rather than -24.4 m (which is the distance between where it is nowto the ground). Since you were using this second bit tocalculate the time taken, you would have to account for the factthat it is moving at this point, so vo is not equal to0. So, if you use -12.6 = -4.9t2, we get that t =1.603567451s when he sees it. So, he has 2.747912009s -1.603567451s = 1.144344557s, which is around 1.1s.

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